On the complexity of the boolean minimal realization problem in the max-plus algebra∗

On the Complexity Ofthe Boolean Minimalrealization Problem

One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. We consider a simpliied version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the system matrices are either equal to the max-plus-algebraic zero element or to the max-plus-algebrai...

On the boolean minimal realization problem in the max-plus algebra

The max-plus algebra is one of the frameworks that can be used to model discrete event systems. One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results for a simplified version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models ...

On the boolean minimal realization problem in the max-plus algebra: Addendum

Scaling, Modeling and Traffic Control of a Real Railway Network using Max-plus Algebra and Model Predictive Control

Delay time recovery can increase the efficiency of the railway network and increase the attractiveness of railway transport against other transportation systems. This article presents a new dynamical model of railway system. The proposed model is a discrete event systems that is defined based on the deviation of travel time and deviation of stop time of trains. Due to the existence of multiple ...

Max-Plus algebra on tensors and its properties

In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.